The factors of 29 are the numbers that divide the number 29 exactly without leaving a remainder. The factors of 29 can be positive or negative, but they cannot be decimal or fractions. For example, the pair factor of 29 can be (-1, -29) or (1, 29). The product of numbers on the negative pair, such as multiplying -1 and -29 results in the original number 29. Here, we will learn the pair factors and the prime factors of 29 and the method of finding the factors of 29 using the prime factorization method and the division method.
Table of Contents:
- What are the Factors of 29?
- Pair Factors of 29
- Factors of 29 by Division Method
- Prime Factorization of 29
- Solved Examples
- FAQs
What are the Factors of 29?
The factors of 29 are the numbers that divide the number exactly without leaving any remainder. In other words, the numbers which are multiplied in pairs will give the product 29. The factors of 29 are 1 and 29. Since the number 29 is a prime number, the factors are one and the number itself.
Factors of 29: 1 and 29 Prime Factorization of 29: 1×29 or 29^{1} |
Pair Factors of 29
As discussed above, the pair factors of 29 can be positive as well as negative. The pair factors of 29 are the pair of numbers, which on multiplication gives the original number 29. The following is the positive pair factor of 29.
Positive Factors of 29 |
Positive Pair Factors of 29 |
1 × 29 |
(1, 29) |
Likewise, the negative pair factor of 29 is given as follows:
Negative Factors of 29 |
Negative Pair Factors of 29 |
-1 × -29 |
(-1,-29) |
Factors of 29 by Division Method
The process of finding the factors of 29 using the division method is discussed below. In this method, we have to divide the number 29 by different numbers, which leaves the remainder 0. The number should divide 29 exactly is considered as the factor of 29.
- 29/1 = 29 (Remainder is 0, and factor is 1)
- 29/29 = 1 (Remainder is 0, and factor is 29)
If we divide 29 by any numbers other than 1 and 29, 29 is not divided completely and it leaves the remainder. Thus, the factors of 29 are 1 and 29.
Also, read: |
Prime Factorization of 29
The process of writing the number as the product of its factors is called the factorization of a number. Similarly, the prime factorization of a number is the method of writing the number as the product of its prime factors. The procedure for finding the prime factorization of 29 is given below.
Step 1: Write down the pair factor of 29, say (1, 29)
Step 2: In this step, we have to check whether the numbers in the pair factor are prime numbers or composite numbers. In the pair factor (1, 29), both the numbers 1 and 29 are prime factors and hence it cannot be split further.
Now, write down the numbers in the form of the product of its prime factors.
Thus, 29 can be written as 1 × 29.
Therefore, the prime factorization of 29 is 1 × 29 or 29^{1}.
Note:
If the numbers in the pair factor are composite numbers, then split the composite numbers into their prime factors and then write it as the product of the prime factors.
Examples
Example 1:
Find the common factors of 29 and 23.
Solution:
The factors of 29 are 1 and 29.
The factors of 23 are 1 and 23.
Thus, the common factor of 29 and 23 is 1.
Example 2:
Find the common factors of 29 and 31.
Solution:
Factors of 29 = 1 and 29
Factors of 31 = 1 and 31.
As both the numbers 29 and 31 are prime numbers, the common factor of 29 and 31 is 1.
Example 3:
Find the common factors of 29 and 58.
Solution:
The factors of 29 are 1 and 29.
The factors of 58 are 1, 2, 29 and 58.
Therefore, the common factors of 29 and 58 are 1 and 29.
Frequently Asked Questions on Factors of 29
What are the factors of 29?
The factors of 29 are the numbers that divide the number 29 exactly without leaving any remainder. The factors of 29 are 1 and 29.
What is the prime factorization of 29?
The prime factorization of 29 is 1 × 29 or 29^{1}.
Write down the positive and negative pair factors of 29.
The positive and negative pair factors of 29 are (1, 29) and (-1, 29), respectively.
Is 13 a factor of 29?
No, 13 is not a factor of 29. As 29 is a prime number, the factors of 29 are 1 and the number itself.
What is the least factor of 29?
The least factor of 29 is 1. 1 is a factor of all the natural numbers.